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Course info
KME / MHP
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Course description
Department/Unit / Abbreviation
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KME
/
MHP
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Modeling of heterogeneous media
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
5
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
2
[Hours/Week]
Tutorial
2
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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Yes in the case of a previous evaluation 4 nebo nic.
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Included in study average
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YES
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Language of instruction
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Czech
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Occ/max
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Automatic acceptance of credit before examination
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Yes in the case of a previous evaluation 4 nebo nic.
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Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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0 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Summer semester
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Semester taught
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Summer semester
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Minimum (B + C) students
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10
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
No
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Fundamental course |
Yes
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Fundamental theoretical course |
No
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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KME/MMB
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Histogram of students' grades over the years:
Graphic PNG
,
XLS
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Course objectives:
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The course intended for students in mechanics and mathematics is aimed at explaining the methodology of modeling the continua which are characterized by heterogeneities at lower scales, teaching students the backgrounds of the homogenization and other approaches employed in the multiscale modeling. Above all the course is focused on modeling the porous materials where at the microscopic level mechanical interactions between interstitial fluids and a solid skeleton take place. The goal is to teach the students, how the theoretical approaches can be adopted for treatment of selected applications in material modeling.
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Requirements on student
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to work-out a quality seminary project,
active knowledge of the stuff delivered in the course lectures, ability to apply the theory in simple examples.
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Content
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1) Introduction - heterogeneous media, examples of applications in biomechanics, geomechanics, composite materials.
2) The notion of the scale, reference volume element,, multiscale description, averaging
3) Diffusion in porous media, various approaches, the Darcy law
4) Fluid saturated porous solids, historical remarks, conservation laws, phenomenological theory.
5) Biot continuum, various parameters and the links between them, basic 1D problems
6) Multiphase theory of mixtures, mechano-chemo-electric interactions, extended Darcy law.
7) Introduction to the asymptotic analysis with respect to the scale parameter, 1D continuum.
8) Homogenization method for periodic structures, formal asymptotic expansion technique.
9) Two-scale convergence, "unfolding" metod and its application for perforated and strongly heterogeneous materials.
10) Waves in heterogeneous elastic media, dispersion.
11) Metamaterials: phononic a photonic crystals, band gaps.
12) Multiscale modeling applied in the tissue biomechanics - bones, tissue blood perfusion.
13) Processing and evaluation of material micrograph images for microstructure reconstruction.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Recommended:
Cioranescu, Doina; Donato, Patrizia. An introduction to homogenization. 1st ed. Oxford : Oxford University Press, 1999.
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Recommended:
Hornung, Ulrich. Homogenization and porous media ; Ulrich Hornung. New York : Springer, 1997. ISBN 0-387-94786-8.
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Recommended:
Coussy, O. Mechanics of Porous Continua, John Wiley & Sons, 2nd Edition. 1995.
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Recommended:
Sanchez-Palencia, E. Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics 127,Springer,. Berlin, 1978.
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Recommended:
Boer, Reint de. Theory of porous media : highlights in historical development and current state. Berlin : Springer, 2000. ISBN 3-540-65982-X.
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On-line library catalogues
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Contact hours
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52
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Graduate study programme term essay (40-50)
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45
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Preparation for an examination (30-60)
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40
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Total
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137
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
assumed skills essentials in the mathematical analysis and tensor calculus, basics in PDE |
assumed skills basics in mechanics, especially in continuum mechanics |
assumed skills basics in numerical methods employed in computational mechanics |
znát základy variačního počtu a orientovat se v základních pojmech funkcionální analýzy |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
formulovat počáteční a okrajové úlohy mechaniky kontinua |
sestavit algoritmus řešení nelineárních soustav algebraických rovnic |
řešit počáteční a okrajové úlohy pro lineární obyčejné diferenciální rovnice |
řešit počáteční a okrajové úlohy pro lineární parciální diferenciální rovnice Fourierovou metodou |
formulovat bilanční vztahy extenzivních veličin pro kontrolní oblast |
řešit jednoduché limitní přechody |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
be able to use the multiscale approach of modeling |
to understand multiscale description of deforming porous media saturated by fluids |
to able to use standard methods of numerical multiscale modeling |
vysvětlit podstatu metody homogenizace periodických prostředí |
Skills - skills resulting from the course: |
to apply the homogenization method for non-complicated examples involving linear diffusion, elastostatics, elastodynamics |
použít metodu homogenizace pro numerický výpočet efektivních elastických parametrů periodicky heterogenních kompozitů nebo výpočet parametrů jejich tepelné a elektrické vodivosti |
použít model Biotova typu pro řešení úloh deformace porézního prostředí nasyceného tekutinou |
Competences - competences resulting from the course: |
N/A |
N/A |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Seminar work |
Skills - skills achieved by taking this course are verified by the following means: |
Combined exam |
Seminar work |
Competences - competence achieved by taking this course are verified by the following means: |
Combined exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Practicum |
Textual studies |
Skills - the following training methods are used to achieve the required skills: |
Lecture |
Practicum |
Competences - the following training methods are used to achieve the required competences: |
Lecture |
Practicum |
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